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Gradient Descent Optimization Game

Interactive optimization game on 2D cost surfaces. Control learning rate to guide parameters to the global minimum without overshooting.

Concept Breakdown: Supervised vs Unsupervised Model Training

1. The Hiker in Fog (Gradient Descent)

Imagine you are hiking down a mountain in pitch-black fog. You feel the slope with your feet and step downward. Gradient Descent does this mathematically — taking steps downhill until reaching the valley floor of lowest error.

2. Measuring Mistakes (Confusion Matrix)

When an AI spots spam emails, it can make two mistakes: letting spam through (False Negative) or blocking a real email (False Positive). A Confusion Matrix tracks these tradeoffs.

3. Try Rolling the Ball!

Click "Step (1 Iteration)" below. Watch the ball take mathematical steps down the parabolic curve until it settles comfortably at the bottom minimum!

Learning Rate (α):0.20
Current Position (θ)-2.000
Current Loss J(θ)17.000
Goal: Reach global minimum at θ = 2.000
COST FUNCTION SURFACE: $J(\theta) = (\theta - 2)^2 + 1$
Min (2.0)

Quick Reference & Instructions

Simple steps, pro tips, and execution details

1

Provide Inputs

Type, paste, or select your values in the form fields below.

2

Instant Live Analysis

Calculations and formatting happen automatically with zero delay as you type.

3

Copy or Use Output

Copy results or apply the clean output directly to your projects.

How It Works

Simulates gradient descent steps on quadratic and non-convex loss curves, highlighting under-shooting, optimal descent, and divergence.

Formula & Logic

θt+1=θt−α∇J(θt)\theta_{t+1} = \theta_t - \alpha \nabla J(\theta_t)

Frequently Asked Questions

Common questions about calculations, assumptions, and edge cases.

Yes, Gradient Descent Optimization Game is 100% free with unlimited calculations and zero paywalls or subscriptions.

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